论文标题
校准HJM前曲线中深度学习的准确性
Accuracy of Deep Learning in Calibrating HJM Forward Curves
论文作者
论文摘要
我们为商品市场上的远期合同中写的欧洲风格的期权定价，我们以无限的希思·贾罗 - 摩尔顿（HJM）方法对此进行了建模。为此，我们介绍了一类新的状态依赖性波动率操作员，该操作员将正方形的集成噪声映射到前向曲线的Filipović空间中。为了进行校准，我们指定了模型的完全参数化版本，并训练神经网络以将真正的选项价格近似为模型参数的函数。然后，该神经网络可以根据观察到的期权价格来校准HJM参数。我们根据确定性波动率设置的人工产生的期权价格进行了数值案例研究。在这种情况下，我们得出了封闭的定价公式，使我们能够基于神经网络的校准方法进行基准测试。我们还研究了流动性不足市场的校准，并进行了大量的出价差异。实验揭示了校准后恢复价格的高度准确性，即使模型参数的原始含义在近似步骤中部分丢失了。
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility operators that map the square integrable noise into the Filipović space of forward curves. For calibration, we specify a fully parametrized version of our model and train a neural network to approximate the true option price as a function of the model parameters. This neural network can then be used to calibrate the HJM parameters based on observed option prices. We conduct a numerical case study based on artificially generated option prices in a deterministic volatility setting. In this setting we derive closed pricing formulas, allowing us to benchmark the neural network based calibration approach. We also study calibration in illiquid markets with a large bid-ask spread. The experiments reveal a high degree of accuracy in recovering the prices after calibration, even if the original meaning of the model parameters is partly lost in the approximation step.
